Appendix D 



Evaluation of the Effects of Composite 

 Sampling on Statistical Power of a Sampling 



Design 



Tetra Tech (1986b) used simulation methods to make a direct com- 

 parison of grab and composite-sampling strategies. Simulation refers 

 to the use of numerical techniques to generate random variables with 

 specified statistical properties. For the analyses described below, Tetra 

 Tech (1986b) developed computer programs to: 1) produce individual 

 random samples from populations with normally distributed con- 

 centrations of contaminants, and other statistical properties similar to 

 those of historical bioaccumulation data sets described in Tetra Tech 

 (1986b), 2) construct composite samples, and 3) calculate statistical 

 power of sampling designs using individual or composite samples. 



Two sets of analyses were performed by Tetra Tech ( 1986b) . In the first 

 set, simulation methods were used to show the effect of sample com- 

 positing on the estimate of the population mean. Power analyses were 

 used in the second set of analyses to demonstrate the effect of increas- 

 ing the number of subsamples in a composite sample on the probability 

 of detecting specified levels of differences among stations. 



The first set of analyses demonstrated that the confidence in the 

 estimate of the mean increases as the number of subsamples in the 

 composite increases (Figure D-1). The simulated sampling consisted 

 of randomly selecting 10,000 composite samples from two populations 

 exhibiting two different levels of variability in the sampling environ- 

 ment. The mean value in both populations was fixed at 18.52, but the 

 population variances were set at 70.90 or 354.19, corresponding to 

 coefficients of vju-iation of 45.5 and 101.6, respectively. These popula- 



